Abstract
In Chaps. 1–3 estimation methods for 1-year default probabilities have been presented. In many risk management applications a 1-year default probability is not sufficient because multi-year default probabilities or default probabilities corresponding to year fractions are needed. Practical examples in the context of retail loan pricing and risk management are presented in Chaps. 17 and 18. In other applications, like credit risk modelling, rating transitions, i.e. the probability that a debtor in rating grade i moves to rating grade j within a period of time, are of importance. In all cases, a 1-year transition matrix serves as the starting point.
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Notes
- 1.
Note that by log(x) we mean the inverse of exp(x), not the logarithm to the base ten.
- 2.
This is not true in general because there are cases where it is still possible to compute transition matrices for arbitrary time periods if the 1-year matrix contains zeros. The simplest example is the identity matrix. However, basically for all practically relevant cases it is true that no consistent t-year transition matrix can be computed from the one-year matrix where t is an arbitrary year fraction.
- 3.
Note that our conclusion is contrary to Jafry and Schuermann (2004). In their analysis they end up recommending the duration method. However, it is not so clear in their article why the duration method should be superior. They basically show that in practical applications like portfolio credit risk modelling it makes a considerable difference if one uses a transition matrix based on the cohort method or based on the duration method. They do not analyze, however, if this difference comes from an estimation bias in the results for the duration method which is our conjecture.
References
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Kreinin A, Sidelnikova M (2001), Regularization Algorithms for Transition Matrices, Algo Research Quarterly 4, pp. 23–40.
Moody’s (2008), Corporate Defaults and Recovery Rates 1920–2007.
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© 2011 Springer-Verlag Berlin Heidelberg
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Engelmann, B., Ermakov, K. (2011). Transition Matrices: Properties and Estimation Methods. In: Engelmann, B., Rauhmeier, R. (eds) The Basel II Risk Parameters. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16114-8_6
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DOI: https://doi.org/10.1007/978-3-642-16114-8_6
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